损伤粘弹性力学的广义变分原理及应用

从粘弹性材料的Boltzmann迭加原理和带空洞材料的线弹性本构关系出发,提出了一种损伤粘弹性材料具有广义力场的本构模型．应用变积方法得到了以卷积形式表示的泛函,并建立了损伤粘弹性固体的广义变分原理和广义势能原理．把它们应用于带损伤的粘弹性Timoshenko梁,得到了Timoshenko梁的统一的运动微分方程、初始条件和边界条件． 这些广义变分原理为近似求解带损伤的粘弹性问题提供了一条途径．     

新型空间薄壁梁单元

基于Timoshenko梁理论和Vlasov薄壁杆件约束扭转理论,建立了具有内部结点的新型空间薄壁截面梁单元．通过对弯曲转角和翘曲角采取独立插值的方法,考虑了横向剪切变形,扭转剪切变形及其耦合作用,弯曲变形和扭转变形的耦合以及二次剪应力等因素影响,由Hellinger-Reissner广义变分原理,推得单元刚度矩阵．算例表明所建模型具有良好的精度,可用于空间薄壁杆系结构的有限元分析．     

不同模量横力弯曲梁的解析解

选择处于平面复杂应力状态下横力弯曲梁,对结构进行了中性层的判定,推导出中性轴、正应力、剪应力、位移的计算公式,得到如下结论:对于复杂应力状态下的不同模量弹性弯曲梁,其中性轴位置与剪应力无关,因此用正应力作为判据而得到解析解,改进了以往用主应力判定中性点的多次循环的计算方法．把解析解的结果与经典力学同模量理论,以及有限元数值解进行了比较,结果表明:解析解很好地考虑了拉压不同模量的效应．还提出了对不同模量结构的计算修正以及对结构优化的思想．     

Euler型梁-柱结构的非线性稳定性和后屈曲分析

在有限变形的假设下,建立了位于非线性弹性基础上非线性弹性Euler型梁-柱结构的广义Hamilton变分原理,并由此导出了任意变截面Euler型梁-柱结构的3维非线性数学模型,其中考虑了转动惯性、几何非线性、材料非线性等因素的影响．作为模型的应用,分析了弹性基础上一端完全固支另一端部分固支,并受轴力作用的均质等截面线性弹性Euler型梁的非线性稳定性和后屈曲;结合打靶法和Newton法,给出了一种计算平凡解(前屈曲状态)、分叉点(临界载荷)和分叉解(后屈曲状态)的数值方法,对前两个分支点和相应分支解,成功地实现了数值计算,并考虑了基础反力和惯性矩对分支点的影响．     

损伤粘弹性Timoshenko梁的拟静态力学行为分析

从考虑损伤的粘弹性材料——一种卷积型本构关系出发,应用Timoshenko梁的基本变形假设,建立损伤粘弹性Timoshenko梁的静、动力学行为研究的数学模型.分析了损伤粘弹性Timoshenko梁在阶跃载荷作用下的准静态力学行为,在Laplace域中得到了挠度和损伤的解析表达式．应用数值逆变换技术,考察了材料粘性参数对梁的挠度和损伤的影响,得到不同时刻损伤和挠度随时间的变化曲线．     

环境自然激励下一种结构损伤在线识别方法

提出了一种环境自然激励下工程结构损伤识别方法,该法仅仅通过结构的输出数据识别结构的损伤．首先在结构完好的情况下,通过结构的输出数据识别外部统计参数;然后在结构损伤情况下,通过结构的输出数据识别结构的损伤分布函数．给出了识别结构损伤的理论模型和计算方法．数值仿真结果表明,该方法具有较高的辨别率和计算精度,能够使用在桥梁和建筑的健康监测中．     

用截面变形耦合有限元法分析复合材料梁

复合材料板和梁具有优良的特性, 从而获得了广泛的应用．然而由于材料的各向异性, 使得对这类材料构件作变形和应力分析时,即使应用如有限元法的数值分析手段仍是非常复杂费时的．为此提出了一个可应用常规有限单元法,分析等截面复合材料梁承受均匀拉弯扭载荷的一个简单精确分析的实施方法．由于巧妙地利用了变形的对称特性,使得分析只需建立在梁的一个切片构造的几何模型上,用常规三维实体有限单元进行结构离散．推导了精确的变形场模式,并借助结构平移自由度的耦合关系使得数值分析易于实施．并通过数值算例来阐明方法的实施过程．     

含分层损伤复合材料加筋层合板的分层扩展研究

建立了复合材料加筋结构的后屈曲和分层损伤扩展行为的数值模拟方法．基于Mindlin一阶剪切理论和von-Karman大挠度理论的层合板和层合梁单元，提出了含分层损伤复合材料加筋层合板分层扩展行为的有限元分析方法；利用虚裂纹闭合技术计算分层前缘的总能量释放率，并采用总能量释放率准则分层扩展判据，结合自适应网格移动技术，对在压缩载荷作用下的具有不同加筋形式，不同初始分层面积和形状的加筋板结构分层扩展行为进行了数值模拟研究，在分析中还考虑了加筋刚度、位置和分布，分层形状和大小、边界支撑强弱和分层前缘的接触效应对结构分层扩展行为的影响．本所提出的研究方法对工程界关于复合材料结构的设计具有重要意义．     

基于剪切效应纤维梁单元的结构非线性有限元数值模拟

基于Euler-Bernoulli梁理论的经典纤维模型忽略了剪切变形给截面带来的影响,为了得到更加精确的梁单元模型,该文基于考虑剪切效应的纤维梁单元,根据Timoshenko梁理论,推导了该纤维梁单元的刚度矩阵,并结合弹塑性增量理论,同时考虑了几何非线性和材料非线性的双重影响,建立了压弯剪复杂应力状态下结构非线性有限元...     

末端质量作用下变长度轴向运动梁的振动特性

对带集中质量,变长度(或速度)轴向运动梁的振动特性采用两种精确方法求解.首先,对变长度轴向运动Euler(欧拉)梁横向自由振动方程进行化简,通过复模态分析得到本征方程,并在有集中质量的边界条件下得到频率方程,用数值方法求解固有频率和模态函数.然后,采用有限元方法建立运动梁自由振动的方程,求解矩阵方程得到复特征值和复特征向量,结合形函数得到复模态位移.最后,将两种方法的计算结果进行了分析和对比.数值算例的结果表明:不同的轴向运动速度和集中质量对变长度轴向运动梁的振动特性有显著影响,两种计算方法的结果接近且均有效.     

Free vibration analysis of cracked beams by using rigid segment method

This paper deals with the analysis of influence of crack parameters to the modal characteristics of beams at various boundary conditions by using rigid segment method. The beam was discretized by a number of rigid segments which were connected by elastic joints with three degrees of freedom, while the crack was described by cracked element based on fracture mechanics. This model allows detection of coupling between the axial and transverse vibrations under the special boundary conditions. The proposed approach covers both the Euler–Bernoulli and Timoshenko beam model. The efficiency of the method was shown through the few numerical examples.     

Structural Crack Identification Based on the Variational Mode Decomposition北大核心CSCD

In order to enrich the bridge damage detection method and further improve the accuracy of bridge damage identification, a detection method for simply supported beams with cracks under dynamic loads was proposed not based on the complete finite element model. Under the premise of not blocking traffic, the method only needs to analyze and deal with the acceleration responses of the simply supported beam span, which reduces the mounting, dismounting and maintenance of sensors in practical engineering. At the same time, based on the model, an analytical formula of the acceleration at the midspan of the simply supported cracked beam was derived. Based on the theoretical derivation, the instantaneous energy and the mean energy difference were constructed through the variational mode decomposition and the Hilbert transform, and these 2 crack identification indexes were used to effectively identify small cracks with a crack depth ratio of only 5%. Then the influences of different wheel loads, environmental noises and damage degrees on detection results were studied. The results show that: ① the instantaneous frequency has a better recognition effect for crack positions; ② the mean energy difference is sensitive to crack depth ratio δ and the wheel load magnitude; ③ this method has strong noise robustness. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Detection of matrix cracks in composite laminates by using the modal strain energy method

As the foremost mechanism of damage development, matrix cracking is the critical damage found in the early stage of structural failure of composites. This study aims to nondestructively detect matrix cracks in composite laminates by using an experimental modal analysis (EMA). An AS4/PEEK composite was used to fabricate cross-ply [0₂/90₁₂/0₂] and quasi-isotropic [(±45/0/90)₄] _s laminates. The damage in the form of a matrix crack in the laminates was created by using a tensile load. The EMA was conducted on the laminates to obtain the modal displacements before and after damage. The displacements were then employed to compute the modal strain energy and to define the damage index, which is used for detecting matrix cracks. Limited by the mesh points of measurements, we used the differential quadrature method to calculate the partial differentials in the strain energy formula. The results obtained were validated by using the X-ray radiography method and three-point bending tests. The experimental results showed that the damage index well identified the location of breadthwise matrix cracks inside the laminates. However, the resolution of the damage index became poor if the spans of matrix cracks were short or the matrix cracks were scattered over the laminates.     

Vibration analysis of cracked post-buckled beams

Vibration analysis of cracked post-buckled beam is investigated in this study. Crack, assumed to be open, is modeled by a massless rotational spring. The beam is divided into two segments and the governing nonlinear equations of motion for the post-buckled state are derived. The solution consists of static and dynamic parts, both leading to nonlinear differential equations. The differential quadrature has been used to solve the problem. First, it is applied to the equilibrium equations, leading to a nonlinear algebraic system of equations that will be solved utilizing an arc length strategy. Next, the differential quadrature is applied to the linearized dynamic differential equations of motion and their corresponding boundary and continuity conditions. Upon solution of the resulting eigenvalue problem, the natural frequencies and mode shapes of the cracked beam are extracted. Several experimental as well as numerical case studies are performed to demonstrate the effectiveness of the proposed method. The investigation also includes an examination of several parameters influencing the dynamic behavior of the problem. The results show that the position and size of the crack as well as the geometric imperfection and applied load largely affect the modal shapes and natural frequencies of the beam.     

Influence of Multiple Micro Cracks on the Damage Behavior of a Macro-Crack Tip北大核心CSCD

The solution of an infinite plane containing a macro crack and a cluster of micro cracks under uniaxial tensile load was presented based on Muskhelishvili’s complex function method and the stepwise recursive method. The stress field and stress intensity factor K were obtained. Combined with the damage mechanics, damage parameter D of the macro-crack tip and the micro-crack tip under uniaxial tension was redefined, and the influence of different damage zone forms on the damage of the crack tip was analyzed. The results show that, both the chain-distribution and the reverse-chain-distribution micro cracks have an amplifying effect on the macro crack growth, and the damage parameter increases with the decrease of the inclination angle of the micro crack and the reduction of the distance between the macro crack and the micro cracks. For a relatively small inclination angle of the micro crack, the damage parameters of the macro crack and the micro crack heightens, and the damage parameter of the macro crack increases with the micro-crack length. For evenly distributed micro cracks in the continuous damage zone, the micro cracks have an amplifying effect on the macro-crack growth, and the damage parameter of the macro crack increases with the micro-crack number. © 2022 Editorial Office of Applied Mathematics and Mechanics. All rights reserved.     

Identification of crack in a rotor system based on wavelet finite element method

The dynamics and diagnosis of cracked rotor have been gaining importance in recent years. In the present study a model-based crack identification method is proposed for estimating crack location and size in shafts. The rotor system has been modeled using finite element method of B-spline wavelet on the interval (FEM BSWI), while the crack is considered through local stiffness change. Based on Rayleigh beam theory, the influences of rotatory inertia on the flexural vibrations of the rotor system are examined to construct BSWI Rayleigh beam element. The slender shaft and stiffness disc are modeled by BSWI Rayleigh–Euler beam element and BSWI Rayleigh–Timoshenko beam element, respectively. Then the crack identification forward and inverse problems are solved by using surface-fitting technique and contour-plotting method. The experimental examples are given to verify the validity of the BSWI beam element for crack identification in a rotor system. From experimental results, the new method can be applied to prognosis and quantitative diagnosis of crack in a rotor system.     

一种裂纹梁振动响应分析的近似方法

本文以线弹簧模型为基础提出了一种近似分析裂纹梁振动响应的方法.把该方法同Euler-Bernoulli梁理论、模态分析方法以及断裂力学原理等结合起来运用,导出裂纹梁振动的特征方程.作为应用实例,本文考核了简支裂纹梁和悬臂裂纹梁的固有频率响应.结果表明,本文所获得的解与现有文献中的解或实验结果取得很好的一致.     

Causes of the damage created by laser pulses in transparent polymers

The characteristics of the damage created in PMM, PS, and PC specimens by multiple irradiation are discussed. It is shown that, in addition to the growth of the damage zone, the processes of crack development that determine this zone are also important. The damage created in PMM when the laser beam is interrupted by a cylindrical cavity is considered. In this case, the cavity acts as a diverging lens and the damage beyond it is determined by the scattered flux. The damage produced in specimens of different shapes is investigated. A model is proposed for crack development in a polymer irradiated by a powerful flux. The model is consistent with most of the known experimental facts.Mekhanika Polimerov, Vol. 3, No. 6, pp. 1035–1042, 1967     

四点弯曲压电梁导电裂纹尖端附近的横观各向同性损伤

根据电焓密度函数建立了压电材料静态损伤本构模型,详细讨论了横观各向同性力电损伤的一些特征,最后通过对四点弯曲PZT-PIC151梁跨中导电裂纹附近横观各向同性损伤的数值分析,研究了裂纹深度和外加力、电载荷对损伤分布的影响规律．结果表明:裂纹深度和力载荷对力电损伤都有非常明显相似的影响,随着裂纹深度和力载荷的增大,裂纹尖端的力电损伤明显增大,范围也相应扩大;电载荷对力损伤完全不同于对电损伤的影响,电载荷单调地改变裂纹尖端力损伤的大小,不改变力损伤的区域尺寸,但是对电损伤的影响则比较复杂．